A Frequency†Domain Test to Check Equality in Spectral Densities of Multiple Time Series With Unequal Lengths

In this paper, a new frequency†domain test is proposed to check the equality of spectral densities of two or more stationary time series. The proposed test is able to deal with multiple independent time series of different lengths naturally, based on some regression models of log periodograms. The asymptotic null distribution of the proposed test is obtained. The consistency is shown under any fixed alternative and a sequence of local alternatives. A simulation study is conducted to examine the finite sample performance of the test. By jointly modeling all log periodograms, the test is empirically robust when multiple time series are mutually dependent to some extent. It also works well for non†Gaussian time series. The proposed test is applied to compare several vibrational signals for damage detection of a mechanical system.